The Annals of Statistics

Manifold estimation and singular deconvolution under Hausdorff loss

Christopher R. Genovese, Marco Perone-Pacifico, Isabella Verdinelli, and Larry Wasserman

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We find lower and upper bounds for the risk of estimating a manifold in Hausdorff distance under several models. We also show that there are close connections between manifold estimation and the problem of deconvolving a singular measure.

Article information

Ann. Statist., Volume 40, Number 2 (2012), 941-963.

First available in Project Euclid: 1 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62H12: Estimation

Deconvolution manifold learning minimax


Genovese, Christopher R.; Perone-Pacifico, Marco; Verdinelli, Isabella; Wasserman, Larry. Manifold estimation and singular deconvolution under Hausdorff loss. Ann. Statist. 40 (2012), no. 2, 941--963. doi:10.1214/12-AOS994.

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